India won the toss and elected to bowl first, and also made a poor start to its chase. It was struggling at 72-5 before top-scorer Mahendra Singh Dhoni arrived at the crease to steady the innings and provide the only spark. He hit 48 off 43 balls with a boundary and three sixes but India managed just 140-6.
Opening partner David Warner made a quick-fire 25 from 14 balls before being caught by Suresh Raina off Vinay Kumar.
George Bailey, the first Australian since 1877 to be made captain in his international debut, finished at 12 not out.
India debutant Rahul Sharma had to leave Olympic Stadium to treat an injured hand in the ninth over after dropping a Travis Birt chance. The leg-spinner returned to bowl the final over and claim the wicket of Hussey to finish with 1-27.
India opener Virender Sehwag continued his run of poor form in Australia, falling for just 4 off the fourth delivery of the chase to Brett Lee.
Former test spinner Brad Hogg (1-21), aged 40, marked his first international T20 since 2007 by claiming the key wicket of Virat Kohli for 22.
The next Twenty20 will be on Friday at Melbourne.